Circular structures are abundant in Molecular Biology.
Circular DNA/RNA molecules include bacterial and archaeal genomes, plasmids (small circular structures in bacteria and archaea used as vectors to transfer genetic information between them), plastomes (the genomes of plastids such as chloroplasts), mitochondrial DNA and some viral genomes.
Circular proteins also exist and circular permutations occur in linear protein structures.
Therefore, the issue of the accurate alignment of such structures is of great importance. This is because current alignment algorithms are solely for linear sequences and if applied to circular sequences, it would add another level of complexity to the analysis, increasing computational cost beyond realistic limits.
I will be publishing quite a few posts about this problem. Have a read of my group's paper introducing an efficient tool for Multiple Circular Sequence Alignment:
C. Barton, C. S. Iliopoulos, R. Kundu, S. P. Pissis, A. Retha, F. Vayani, "Accurate and efficient methods to improve multiple circular sequence alignment", in Experimental Algorithms, E. Bampis, Ed., Springer International Publishing Switzerland, 2015, pp. 247-258